How do you find the inverse of #f(x)=(6x+4)/(4x+5)# and graph both f and #f^-1#?

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Answer 1 · 2017-03-04T10:52:55

The inverse is #f^-1(x)=(4-5x)/(4x-6)#

We have

#f(x)=(6x+4)/(4x+5)#

Let #y=(6x+4)/(4x+5)#

Therefore,

#y(4x+5)=6x+4#

#4xy+5y=6x+4#

#4xy-6x=4-5y#

#x(4y-6)=(4-5y)#

#x=(4-5y)/(4y-6)#

So,

The inverse of #f(x)# is

#f^-1(x)=(4-5x)/(4x-6)#

graph{(y-(6x+4)/(4x+5))(y-(4-5x)/(4x-6))(y-x)=0 [-8.89, 8.89, -4.44, 4.45]}